**prime number factorization**i.e

**. “Dixon’s prime factorization” .**

**prime factorization**is the breaking of a composite number into smaller co-primes, which when multiplied together then become the original integer.

**integer factorization algorithm**is used.These type of algorithms are based on the difficulty of

**factoring large composite integers**or a related problem, the

**“RSA problem”.**

**Dixon’s algorithm”**in which it will give the factors of those prime numbers which are the multiples of semi-primes.

#### How to run the implementation of Dixon’s Algorithm

**Steps:**

**1)**Open the notepad and copy the code there and save it with .java extension (say Exe.java).

**2)**Install the java software(if not present in your PC).

**3)**Open the command prompt.

**4)**Compile this .java file (Exe.java ) in the cmd by using the command javac (ex : javac Exe.java ).

**5)**Run this file by using “java” command (ex: java Exe)

**6)**Input a number which is the factor of 2 semi primes.

**7)**Then see the result……it will display the factors of this original number.(checked for the prime numbers upto 11 digit number)

import java.util.Scanner;

class Exe

{

public static void main(String args[])

{

Scanner ob=new Scanner(System.in);

System.out.print("n------------------n!! ENTER THE NO. !! : ");

double n=ob.nextDouble();

System.out.println("n ---------------------------------------------");

dixon(n);

}

public static double gcd(double a,double b)

{

if(b==0)

return a;

else if(b>a)

return gcd(b,a);

else

return gcd(b,a%b);

}

public static int checkprime(double n)

{

int f=0;

for(int i=2;i<=n/2;i++)

{

if(n%i==0)

{

f=1;

break;

}

}

if(f==1)

return 0;

else

return 1;

}

public static void dixon(double n)

{

int a,d,b1,d1;

double m,x,p,q;

m=Math.sqrt(n);

double c=Math.floor(m);

int f1=0;

for(double f=c+1;f<=n;f++)

{

double s,m1;

s=Math.sqrt((f*f)%n);

m1=Math.floor(s);

if((s-m1)==0)

{

if(s!=(f%n))

{

p=f+s;

q=f-s;

b1=checkprime(p);

d1=checkprime(q);

if(b1==1)

{

double z=gcd(q,n);

int b=checkprime(z);

if(b==1){

System.out.println(" -----------------------------------------------------");

System.out.println(" THE TWO FACTORS ARE "+z+" and "+p);

System.out.println(" ------------------------------------------------------");

}

}

else if(d1==1)

{

double z=gcd(p,n);

int b=checkprime(z);

if(b==1){

System.out.println("---------------------------------------------");

System.out.println(" THE TWO FACTORS ARE "+z+" and "+q);

System.out.println("---------------------------------------------");}

}

else

System.out.println("--------------- NEITHER OF THE FACTORS ARE PRIME---------" );

f1=1;

break;

}

}

if(f1==1)

break;

}

}

}

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